1 of 8 0-day streak

Analyse exponential and logarithmic graphs

Question 1 of 8

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The function below is to be described using exact coordinates and transformations

f(x)=\log_{\frac{625}{256}}\left(x\right)

The basic family has base \(\frac{625}{256}\). The two marked exact points used in the feature table are P=\((\frac{625}{256},1)\) and Q=\((\frac{390625}{65536},2)\)

Their basic-family exponent values are \(t=1\) for P and \(t=2\) for Q

(a)1 mark

Select the statement that gives the domain, range and asymptote

The domain is all real numbers, the range is all real numbers, and the asymptote is y=0

The domain is x>0, the range is all real numbers, and the asymptote is y=0

The domain is all real numbers, the range is x>0, and the asymptote is x=0

The domain is x>0, the range is all real numbers, and the asymptote is x=0

(b)1 mark

State whether the graph increases or decreases as x increases

The graph decreases as x increases

The graph increases as x increases

Complete the exact feature table

vertical asymptote coordinate x-coordinate of Q y-coordinate of P x-coordinate of P y-coordinate of Q x-coordinate of the x-intercept